It is clear that by the end of the novel we see that Gradgrind has undergone a 180 degree turn in terms of his beliefs and philosophy. Having discovered that emotions are important and that facts are not the most important thing in the world, Dickens gives us hope for the future of this character as he is left to consider his mistakes in the way he brought up Tom and Louisa and the difficulties and challenges that they face as a result. Note the mention that is made of Gradgrind in the last chapter, which discusses the endings that the various characters face:
Did he see himself, a white-haired decrepit man, bending his hitherto inflexible theories to appointed circumstances; making his facts and figures subservient to Faith, Hope and Charity; and no longer trying to grind that Heavenly trio in his dusty little mills?
The change is clear. His "hiterto inflexible theories" are now bending to circumstances and his "facts and figures," that once held such sway in his life, are now "subservient" to higher and more noble emotions. He has obviously learnt the limitations of trusting in facts alone, and although we are told that this change in character has resulted in his facing scorn from his former political friends, we are assured that he is a happier man as a result.